Kaine topped a list of potential vice president candidates with about 20 percent probability, followed by U.S. Senator Elizabeth Warren of Massachusetts with about 17 percent and U.S. Labor Secretary Tom Perez with about 14 percent.

The website, which allows users to wager small amounts of money, said Sanders' chances of joining Clinton's race for the White House were about 10 percent. Big election wins on Tuesday catapulted Clinton to victory over Sanders, a U.S. senator from Vermont, although he has vowed to go on contesting the race.

Bets on Clinton winning the Nov. 8 U.S. presidential election were going for 66 cents while bets on Donald Trump, the presumptive Republican nominees, were traded at just 33 cents.

On the Republican side, U.S. Senator Jeff Sessions of Alabama was leading the race to be Trump's running mate at 20 percent, followed by U.S. Senator Joni Ernst of Iowa at 17 percent, former House Speaker Newt Gingrich at 15 percent and New Jersey Governor Chris Christie at 9 percent.

See some other potential Clinton running mates:

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Hillary Clinton potential running mates, VPs

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US Senator Tim Kaine an online favorite to run with Clinton

Tim Kaine

The junior Democratic Senator from the swing state of Virginia could be a strategic selection for Hillary. Kaine also served as the governor of Virginia from 2006- 2010.

(Photo by Samuel Corum/Anadolu Agency/Getty Images)

Elizabeth Warren

The current U.S. Senator from Massachusetts is popular among progressive Democrats, and some even tried to draft her to run for president herself in 2016.

(Photo by Andrew Harrer/Bloomberg via Getty Images)

Sherrod Brown

Insiders believe that the senior U.S. Senator from Ohio could help Clinton increase her popularity with working-class voters, a group she has yet to win in a big way so far in primary contests.

(Photo By Bill Clark/CQ Roll Call)

Cory Booker

The U.S. Senator from New Jersey is both youthful and charismatic and would add racial diversity to a Clinton ticket.

(Photo by KK Ottesen for The Washington Post via Getty Images)

Tom Perez

The current U.S. Secretary of Labor is considered a sleeper pick by many Democrats because he is not well known outside of D.C., but some believe his strength and popularity among union workers and other progressive groups could be an asset to Clinton's ticket.

(Photo By Tom Williams/CQ Roll Call)

Bernie Sanders

The Independent from Vermont has become Hillary Clinton's primary rival for the Democratic nomination, garnering a surprising amount of support. Bringing Sanders onto the ticket could help to unite both sets of supporters who have been split in Democratic primaries.

(Photo by Ralph Freso/Getty Images)

Martin O'Malley

A former 2016 rival of Hillary Clinton, and former Maryland governor, Martin O’Malley could help bring some executive experience, along with a slight youthful boost to the ticket.

(Photo by Joe Raedle/Getty Images)

Tom Vilsack

The Secretary of Agriculture since 2009, Tom Vilsack also served as the governor of Iowa from 1999 to 2007. Vilsack could bring some governing experience along with swing state influence.

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Evan Bayh

Evan Bayh could bring a more right leaning brand of politics to the ticket. Bayh previously served as the junior U.S. Senator from Indiana from 1999 to 2011, and also as the 46th Governor of Indiana from 1989 to 1997.

Joe Biden

While the likelihood of him agreeing to take on the veep job again might be low, Biden's popularity among Democrats would likely boost Clinton's chances.

(Photo credit MANDEL NGAN/AFP/Getty Images)

Bill Clinton

Hillary's husband is technically allowed to serve in the job, and some legal experts even think he'd be able to take office if necessary. Unfortunately for the diehard Clinton supporters, a Clinton-Clinton ticket will probably be a dream that never comes true.

The online survey had 44.3 percent of likely voters saying they would vote for Clinton, compared with 34.7 percent who would support Trump. A further 20.9 percent said they would not vote for either candidate.

PredictIt is jointly run by Washington political consultancy Aristotle and Victoria University in Wellington, New Zealand. Its users are registered U.S. voters. As with opinion polls, predictions markets do not always accurately forecast outcome.